NYC taxi meter and options pricing
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The introduction of option pricing theory, terminology and various forms of hand waving does nothing but confuse the central argument with gross misapplication of theory.
The cab driver is constantly playing bird in the hand is worth two in the bush - do I take less per minute with this customer but take a long time, or take the customer quickly, get paid more, but then also have the risk I won’t pick anyone up for long enough that I am worse off?
I think most people go for bird in hand is the issue.
Medallion owners earn more when their cabs complete trips faster. What they pay their drivers is a matter of their contract.
I make this clarification because it has muddied policy waters before. Some cabbies own their medallion. But most are independent contractors to a corporate owner.
In general medallion owners do not "pay their drivers". Most drivers pay the medallion owners to lease the taxicab (or the medallion alone).
I wanted to write an informal introduction to options using a more tangible example for those who are put off by the maths but still would like to gain an intuitive understanding. At the same time I wanted to show things I found were interesting in the data.
It may have been better to separate the two ideas. As you rightly say, one is confusing the other in the current form.
Only if supply is saturated by demand. I'd rather get paid to sit in traffic than be idle.
He's covering a lot of ground and might have done better to lead with the graph that he made with his product, which shows that the average speed of cabs has gone down a lot.
The options curves that he talks about then involve: (1) how does slower driving impact the earnings of cab drivers and (2) is a cab driver motivated to drive faster or slower?
If log-normal distributions, greek coefficients and such were really relevant they should be realized to something like "delta was 0.2 in 2011 and 0.4 in 2012 because of X and with the consequence Y"
I am still left wondering how do the following factors combine:
- increasing traffic from increasing population and economic activity
- increasing traffic from increased ride hailing competition (those yellow cabs have a quota, but the challengers don't)
- increasing traffic from deteriorating conditions on public transit
- cab drivers deciding to drive faster or slower because of what they learned at the Chicago School of Economics
and that's were "gross misapplication of theory" comes in. When profit is the small difference between two large numbers it is easy to lose a whole basketball team's worth of shirts pricing options -- every crisis a new generation of quants learn the hard way that Marx had a point about the "declining rate of profits".
We want more people using taxis rather than their own cars.
The taxi has to drive around between fares, increasing congestion for no benefits to the wider economy.
Also, so far taxis are still all driven by humans. The economy only has a fixed number of humans and needs to allocate them to the most worthwhile things. Having two humans (driver and customer) in a vehicle travelling to a place costs society more than having just one person doing the driving.
Compared to 100 cars to 100 people.
Can you imagine what London would be like tomorrow if everyone suddenly took their car to work? It'd be completely intractable. Nobody would even get near the city centre.
The only difference is the amount of parking needed.
Had the city been built for that (ie. A few floors of underground parking under every building) it would be fine. Some cities in Poland do this. Clearly retrofitting that isn't practical.
Have you actually thought this through?
For example - 6,000 people work at the Gerkin.
Can you guess what area is needed to park 6,000 cars? How many underground levels you'd need? How long would it take cars to filter in at the start of the day and filter out at the end? How much road space you'd need for everyone to get to the building in the first place?
It's 90,000 m^2. That's about 90 underground levels you're building there, or digging twice as deep as the building is high.
Your idea is insane.
In dense areas we need everyone going by space efficient transport (walking, tubes or buses if they are full, maybe bikes)
Yeah I know that I'm not advocating for anyone taking any kind of car...
...but if they're going to take a car we'd prefer it was a taxi not a private car. So a higher proportion of taxis over private cars is a good thing (as long as total number stays the same.)
But I'm not convinced of the merits of that many Ubers in a city with very good public transport and improving active travel options (bike lanes).
I always knew this, but I always assumed it was because of the value of the $2.50 meter drop. I didn't realize how much of an incentive it was built into the meter fare.
This explains why they always drive so crazy.
> A slow-earning loaded cab makes more money than an empty one.
The author ignores significant issues with the data. These include time of day, where time-specific surcharges increase the fare independent of distance or time spent in the taxi. The author also ignores the shift system for fleet cabs. As a general rule, fleet cabs operate two twelve hour shifts, with the day shift generally being less lucrative than the night shift. What's more, the author ignores the fact that Thursday evening through Sunday morning are significantly more lucrative than the rest of the week.
If you ignore the above and just average everything together, you'll miss important differentiators in revenue.
I get that the author normalized the data to enable his analysis of revenue. But given that he ignores important variables makes the results suspect.
Many drivers only drive at night. Many drivers only drive during the day. Some drivers only drive Thursday-Sunday. Some only drive Monday-Friday.
So a Monday-Friday day shift driver will generate less revenue than an Monday-Friday night shift driver. Similarly, a Wednesday-Sunday day shift driver will generate less revenue than a night shift driver.
And those who work Wednesday-Sunday will generate more revenue than those who work Monday-Friday.
And the author focuses only on the revenue side and ignores the costs. The last time I checked, a day shift lease is ~$95+full tank of gas, while a night shift lease is ~$120+full tank of gas, with a premium charged Thursday-Sunday.
However, there are other kinds of leases as well. A weekly lease, generally shared by two drivers, will run ~$900-$1000 split between them. And a monthly lease can be even more cost-effective.
And those leases include maintenance on the vehicle, insurance and vehicle storage.
While it's interesting to see the analysis of how the fee structure generates revenue, the author ignores a whole raft of other variables which directly impact on revenue generation.
Lastly, the author asserts that it's the "antiquated" taxi meter fee structure that has caused drivers to be "progressively worse-off."
I don't see how he was able to draw that conclusion from the data presented.
Edit: Fixed typos and edited for clarity
As for the taxi meter fee structure, Uber/Lyft can work around this with surge fees during those congested peak hours, while taxis cannot. This too is quite clearly in the Uber drivers' favor: if you're going to be sitting around in traffic, better to be paid more for it. (Unless Uber takes all the extra revenue for themselves, but that's another story.)
Probably not. However, if the analysis doesn't provide enough nuance WRT revenue generation, how useful is that analysis, except as a primer on using those particular techniques in a novel fashion?
>At the end of the day the argument boils down to "drivers make more money when they can drive faster", which seems pretty indisputable.
Absolutely a fair point, although ignoring the time-based variations in the demand curve likely has a measurable effect on revenue generation.
To illustrate that point, during the pandemic, overall traffic volumes are down at least 50%, presumably allowing even day time drivers to drive faster. However, some estimates of taxi driver revenue have it down 80+%.
Even more, traffic lights on one-way avenues (at least in Manhattan, where the bulk of medallion taxis operate) are generally set at slightly less than 25 miles/hour (the citywide default speed limit), so "driving faster = making more money" isn't really correct. "Driving faster than 12 miles per hour usually results in higher revenue" is probably more accurate.
>So if overall traffic speeds are slowing down, then in aggregate all drivers will suffer as well, although the daytime driver suffering through rush hour gridlock will be comparatively worse off than a driver who focuses on long airport rides in the middle of the night.
That absolutely applies to day time drivers, and night-time drivers can (and usually do) generate more revenue. However, some of that difference is unrelated to speed. Rather it's related to demand. Because people know that traffic is bad during the day makes them less likely to use a taxi during the day and more likely to do so at night.
However, your example of airport rides is flawed, as rides between airports/Manhattan are a flat fare and not based on time and distance.
I don't use Uber or other FHV services, mainly because I find their business model offensive, given the huge fees they charge are way out of proportion to the services they provide -- and that's fundamentally unfair to the drivers.
Which is also why I always pay cash when using a taxi, as there's usually a fee of at least 5% on credit card transactions in the taxi, and drivers often don't receive their money for days -- yet the fleet owners require up-front payment for leases, and the drivers must fill the gas tank before returning the car.
I lived in NYC prior to Uber and when Uber was first making inroads (for 9 years until 2016, so this totally could have changed since). Often, I'd chat with the driver to pass time/reduce awkwardness. A common complaint was drivers being required to lease a cab for a full-week for 12 hours each day.
>As a general rule, fleet cabs operate two twelve hour shifts, with the day shift generally being less lucrative than the night shift.
Taxi shifts are scheduled and designed so each shift is equally attractive, so that each shift gets a rush hour [1].
As an aside, as someone who works on the software side of the options trading business, I found the article to be quite interesting.
That market really changed from a sellers to a buyers over the years.
Note that I didn't say it was $120 for a premium lease, I said $120 for a night shift lease Sunday-Wednesday, with premiums on top of that for Thursday-Saturday nights.
What's more, the Taxi and Limousine Commission (TLC) that regulates Taxis and For Hire Vehicles (FHV), has capped the maximum lease rates, since every time the fares increased, fleet owners would raise lease rates to take almost all the additional revenue.
I'm not claiming that folks make lots of money driving medallion taxis in NYC (in fact, the bottom has pretty much dropped out during the pandemic).
Rather I don't think that the analysis in the article is nuanced enough to make any comparisons with Uber/Lyft and other FHV drivers.
[0] https://www.nycitycab.com/Business/FleetTaxisforleaseList.as...
This is a pretty unconvincing argument, because increasing the standard deviation increases the expected value of a lognormal distribution, even without any weird option payoffs being involved.
Moreover, a higher standard deviation decreases the compounded returns of a log normal distribution, not decreases it. This is called volatility drag, and is closesly related to the AM-GM inequality: the geometric and arithmetic means of a series are only equal if all terms are identical. If this is not true, an arithmetic average will always be greater.
[0]https://www.marketwatch.com/story/all-hail-new-york-citys-ta...
Or if you prefer Lispy stuff :)
(+ 30 (* 2.5 (max (0 (- speed 12)))))
This then means if you drive at 22mph for 1 hour, you earn 30 + (2.50 * max(0, 10)) or $55 which you also get from 2.50 * 22
Is this just discounting the constant multiplier since it applies to everything and can be pulled out?
> $2.50 x their average speed if they drove above 12mph
Seems like those arent the same... hopefully it isnt both...
> $30 if they drove below 12mph ($0.50 a minute)
Average speed: 30mph => $2.50 * 30 miles = $75
It is the same, because it was already assumed to be based on exactly one hour.
What?? Why would you do it like that? That incentivized jerking up to 12 mph whenever possible.
Uber got this right early on: the rate for the time and mileage are separate.
No it doesn't. Driving 12mph translates to 12 * 2.50 = $30/hour. Driving under 12mph translated to 60 * 0.5 = $30/hour. It's a smooth transition.